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Question

A particle is subjected to two simple harmonic motions, one along the X-axis and the other on a line making an angle of 45 with the X-axis. The two motions are given by

x=x0 sin ωt and s=s0 sin ωt

Find the amplitude of the resultant motion.


A

x20+s20+2x0s0

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B

x0+s0

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C

x0+s02

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D

None of these

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Solution

The correct option is A

x20+s20+2x0s0


The particle is subjected to two simple harmonic motions represented by,

x=x0 sin ωt

s=s0 sin ωt

and, angle between two motions =45

Resultant motion will be given by,

R=(x2+s2+2xs cos 45)

={x20sin2ωt+s20sin2ωt+2x0s0sin2ωt(12)}

=[x20+s20+2x0s0]12sin ωt

Resultant amplitude


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